Cross-correlation dynamics in financial time series

The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined.A basic one-factor model is then proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a ‘market plus sectors’ model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found for empirical data. By partitioning the eigenvalue time series, we then show that negative index returns, (drawdowns), are associated with periods where the largest eigenvalue is greatest, while positive index returns, (drawups), are associated with periods where the largest eigenvalue is smallest. The study of correlation dynamics provides some insight on the collective behaviour of traders with varying strategies.     

Coupled continuous-time random walk approach to the Rachev-Rüschendorf model for financial data

In this paper we expand the Rachev-Rüschendorf asset-pricing model introducing a coupled continuous-time-random-walk-(CTRW)-like form of the random number of price changes. Such a form results from the concept of the random clustering procedure (that resembles the coarse-graining methods of statistical physics) and, on the other hand, indicates applicability of the CTRW idea, widely used in physics to model anomalous diffusion, for describing financial markets. In the framework of the proposed model we derive the limiting distributions of log-returns and the corresponding pricing formulas for European call option. In order to illustrate the obtained theoretical results we present their fitting with several sets of financial data.     

Application of spectral methods for high-frequency financial data to quantifying states of market participants

Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A 382 (2007) 258-270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation of the earth, and that the similarities among best quotation rates are associated with those among quotation frequencies. Furthermore, it is shown that the Jensen-Shannon spectral divergence is proportional to a mean of the Kullback-Leibler spectral distance both empirically and numerically. It is confirmed that these spectral distances are connected with distributions for behavioural parameters of the market participants from numerical simulation. This concludes that spectral distances of representative quantities of financial markets are related into diversification of behavioural parameters of the market participants.     

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that qth-order generalized Hurst exponents h(q) and τ(q) change with the moments q. The nonlinear dependence of these scaling exponents and the singularity spectrum f(α) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.     

Long memory features in the high frequency data of the Korean stock market

This paper examines the long memory property in the high frequency data of KOSPI 200 using the FIAPARCH model. The empirical results indicate that the FIAPARCH model can capture asymmetry and long memory in the volatility of intraday KOSPI 200 returns. Interestingly, the presence of long memory is invariant to the temporally aggregated intraday returns, implying that a long memory phenomenon is an inherent characteristic of the data generating process, not a result of structural breaks.     

Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method

Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes.     

Effects of time dependency and efficiency on information flow in financial markets

We investigated financial market data to determine which factors affect information flow between stocks. Two factors, the time dependency and the degree of efficiency, were considered in the analysis of Korean, the Japanese, the Taiwanese, the Canadian, and US market data. We found that the frequency of the significant information decreases as the time interval increases. However, no significant information flow was observed in the time series from which the temporal time correlation was removed. These results indicated that the information flow between stocks evidences time-dependency properties. Furthermore, we discovered that the difference in the degree of efficiency performs a crucial function in determining the direction of the significant information flow.     

Long term memory in extreme returns of financial time series

It is well known that while daily price returns of financial markets are uncorrelated, their absolute values (‘volatility’) are long-term correlated. Here we provide evidence that certain subsequences of the returns themselves also exhibit long-term memory. These subsequences consist of maxima (or minima) of returns in consecutive time windows of R days. Our analysis shows that for both stocks and currency exchange rates, long-term correlations are significant for R≥4. We argue that this long-term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation.     

Small scale behavior of financial data

A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered distribution to a reference distribution. The existence of a small timescale regime is demonstrated, which exhibits different properties compared to the normal timescale regime for timescales larger than one minute. This regime seems to be universal for individual stocks. It is shown that the existence of this small timescale regime is not dependent on the special choice of the distance measure or the reference distribution. These findings have important implications for risk analysis, in particular for the probability of extreme events.     

Analysis of binarized high frequency financial data

A non-trivial probability structure is evident in the binary data extracted from the up/down price movements of very high frequency data such as tick-by-tick data for USD/JPY. In this paper, we analyze the Sony bank USD/JPY rates, ignoring the small deviations from the market price. We then show there is a similar non-trivial probability structure in the Sony bank rate, in spite of the Sony bank rate's having less frequent and larger deviations than tick-by-tick data. However, this probability structure is not found in the data which has been sampled from tick-by-tick data at the same rate as the Sony bank rate. Therefore, the method of generating the Sony bank rate from the market rate has the potential for practical use since the method retains the probability structure as the sampling frequency decreases.     

Tail distribution of index fluctuations in World markets

We have investigated the tail distribution of the daily fluctuations in 202 different indices in the stock markets of 59 countries for the time span of the last 20 years. Power law, log-normal, Weibull, exponential and power law with exponential cutoff distributions are considered as possible candidates for the tail distribution of the normalized returns. It is found that the power exponent depends strongly on the choice of the tail threshold and a sizeable number of indices can be better fitted by a distribution function other than the power law at the region that has power law exponent of 3. Also, we have found that the power exponent is not an indicator of the maturity of the market.     

Scaling and memory in the return intervals of realized volatility

We perform return interval analysis of 1-min realized volatility defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold q are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks (out of 22 stocks) and the SSEC pass the Kolmogorov-Smirnov (KS) test and exhibit scaling behaviors, among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the KS goodness-of-fit test under the significance level of 5%. The improved scaling behavior is further confirmed by the relation between the fitted exponent γ and the threshold q. In addition, the similarity of the return interval distributions for different stocks is also observed for the realized volatility. The investigation of the conditional probability distribution and the detrended fluctuation analysis (DFA) show that both short-term and long-term memory exists in the return intervals of realized volatility.     

Topological properties of stock networks based on minimal spanning tree and random matrix theory in financial time series

We investigated the topological properties of stock networks constructed by a minimal spanning tree. We compared the original stock network with the estimated network; the original network is obtained by the actual stock returns, while the estimated network is the correlation matrix created by random matrix theory. We found that the consistency between the two networks increases as more eigenvalues are considered. In addition, we suggested that the largest eigenvalue has a significant influence on the formation of stock networks.     

Long memory properties in return and volatility: Evidence from the Korean stock market

In this paper, we study the dual long memory property of the Korean stock market. For this purpose, the ARFIMA-FIGARCH model is applied to two daily Korean stock price indices (KOSPI and KOSDAQ). Our empirical results indicate that long memory dynamics in the returns and volatility can be adequately estimated by the joint ARFIMA-FIGARCH model. We also found that the assumption of a skewed Student-t distribution is better for incorporating the tendency of asymmetric leptokurtosis in a return distribution.     

Weather effects on returns: Evidence from the Korean stock market

In this study, we attempted to determine whether a relationship exists between stock returns and the weather variables of temperature, humidity, and cloud cover in the Korean stock market. We delineated three key implications with regard to weather effects. First, after the 1997 financial crisis, the presence of a weather effect disappeared. Second, the inclusion of weather variables helps to model the GJR-GARCH process in the conditional variance. Third, the interaction effects of weather variables fully demonstrate the weather effect, but the interaction effects also vanished after the crisis. Overall, the findings of this study indicate that the weather effect was weakened as the result of heightened market efficiency.     

An exploration of commonly observed stylized facts with data from experimental asset markets

We analyze data from experimental asset markets with pooled linear regression models to shed some light on the emergence of fat tails and volatility clustering in return distributions. Our data suggest that the arrival of new information is the most important cause for both stylized facts. After new information arrives we see spikes in volatility as this information is digested in the market. We also find that uninformed traders contribute significantly more to fat tails than do informed traders and that the heterogeneity in fundamental information leads to larger returns.     

Globalization — Entropy unification through the Theil index

A time series is remapped onto an entropy concept, based on the Theil index. The Manhattan distance between these surrogate series is calculated, and contrasted to the usual correlation distance measure. The idea is applied to several Gross Domestic Product (relative increments) of rich countries. Such distances are calculated for various time window sizes. The role of time averaging in such finite size windows is discussed. We construct the locally minimum spanning tree (LMST) corresponding to the distance matrix. Another hierarchical network structure (Unidirectional Minimal Length Path) is compared with the LMST for confirming that the mean distance between the most developed countries on different networks actually decreases in time, — which we consider as a proof of economy globalization. It is stressed that this entropy distance measure seems more suitable in detecting some “phase transition” in time series, like a globalization process than the usual correlation based measure.     

Modeling and asset allocation for financial markets based on a discrete time microstructure model

On the basis of the market microstructure theory and the continuous time stochastic volatility-style microstructure model, a discrete time stochastic volatility microstructure model with state-observability is proposed for describing the dynamics of financial markets. From the discrete time microstructure model proposed, estimates of two immeasurable state variables representing the market excess demand and liquidity respectively may be obtained. A simple trading strategy for dynamic asset allocation, based on the indirectly obtained excess demand information instead of the prediction for price, is presented. An approach to the estimation of the discrete time microstructure model using the extended Kalman filter and the maximum likelihood method is also presented. Case studies on financial market modeling and the estimated model-based asset dynamic allocation control for the JPY/USD (Japanese Yen/US Dollar) exchange rate and Japan TOPIX (TOkyo stock Price IndeX) show satisfactory modeling precision and control performance. Received 11 March 2002 / Received in final form 4 November 2002 Published online 4 February 2003 RID="a" ID="a"Currently a visiting researcher at the Institute of Statistical Mathematics, 4-6-7 Minami Azabu, Minato-ku, Tokyo 106-8569, Japan e-mail: peng@ism.ac.jp     

Herd behavior in weight-driven information spreading models for financial market

We study two weight-driven information spreading models for financial market. In these models, we find that the activity threshold below which the ‘financial crash’ occurs can be increased by uneven distribution of information weight, compared with Eguíluz and Zimmermann model [V.M. Eguíluz, M.G. Zimmermann, Phys. Rev. Lett. 85 (2000) 5659]. We also find that below the threshold the normalized return distribution, P(Z;Δt) satisfies P(Z=0;Δt)∼exp(−Δt/b) whereas P(Z=0;Δt)∼Δt^−τ above the threshold. Here Δt is the time interval where the normalized return is defined, Z(t,Δt)=Z(t+Δt)−Z(t). By approximating the relative increase of P(Z;Δt=1) for large Z as Gaussian distribution with non-zero mean, we show that the non-zero mean of the Gaussian distribution can cause such exponentially decaying behavior of P(Z=0;Δt).     

Modeling sudden volatility changes: Evidence from Japanese and Korean stock markets

In this study, we have investigated sudden changes in volatility and re-examined the persistence of volatility in Japanese and Korean stock markets during 1986-2008. Using the iterated cumulative sums of squares (ICSS) algorithm, we have determined that the identification of sudden changes is generally associated with global financial and political events. We have also demonstrated that controlling sudden changes effectively reduces the persistence of volatility or long memory and that incorporating information regarding sudden changes in variance improves the accuracy of estimating volatility dynamics and forecasting future volatility for researchers and investors.